An Agent Based Model of Multifunctional Agricultural Landscape Using Genetic

Algorithms

Seth Soman1, Girmay Misgna2, Chris Lant3,Steven Kraft2, Jeff Beaulieu2, and Raja Sengupta4*

1 Dickinson state university 2 Agribusiness Economics, 3 Geography (SIUC)* 4 McGill University Canada

• Based upon work supported by the National Science Foundation under Grant No. 0410187.

Agricultural landscapes are potentially important producers of ecosystem services e.g., enhanced water quality, nutrient recycling, reduced sedimentation, carbon sequestration, and enhanced wildlife habitat, in addition to traditional agricultural commodities.

Multifunctionality refers to the possibility that an economic activity may have multiple outputs, both commodity and non-commodity outputs and consequently may contribute to societal welfare (OECD 2002).

Problem : Public goods

Ecosystem Services

• Changes in land use, e.g., result in changes in the flow of ecosystem services

A large number of factors affect land owners willingness to change land use decisions to capture ecosystem services (Lockeretz, 1990, Napier, 1991, Kraft and Loftus, 2003)

•Personal characteristics of the farm owner• institutional connection• Economic• Financial incentives• Legal rights.

Modeling farmers as agents

Problem with modeling human choice

Not always maximizing/minimizing or optimizing.

Herbert Simon*: “Bounded Rationality”:limits on knowledge and analytical ability force people to choose the first satisfactory option.

Heterogonous individualsIncome and preferencesintelligence, experience

* H.A. Simon et. al, 1986, Decision Making and Problem Solving. In: Research Briefing Panel on Decision Making and Problem Solving. Washington, D.C., USA: National Academy Press.

-----Lack of spatial information

Thinking Spatially

AgentsWoolridge and Jennings, 1995:

Agent are :

Autonomous

Ability to sense their environment

Ability to act upon their environment

Rational behaviour

Could include humanistic characteristics such as beliefs, desires, intentions (Shoham, 1993) and even emotions (Maes, 1995)

Agent model:: human decision making

Spatial (Pattern-based model): humans are located in geographic space

Human decision making Model

Interaction environments:

• Landscape (Biophysical factors, e.g. soils, crop productivity)

• Political institutions• Social interaction• Markets

Research Objective

1. How well the ABM predict the actual land-use

2. Analyze multiple policy scenarios using the ABM.

Cache Watershed encompasses, 1,944km2 of southern Illinois near the confluence of the Mississippi and Ohio Rivers. The Watershed has diverse ecological resources and unique natural communities. At least 100 state threatened or endangered plant and animal species are known within the watershed (USFWS 1990).

Endangered species: Cypress and Tupelo Swamps

Study Area

Big Creek Watershed

Comprises two main creeks:

Big Creek (29 km)

Little Creek (15 km)

The Big Creek is a tributary of the Lower Cache River with a drainage area of 33,088 acres (51.7 square miles).

Loss and fragmentation of natural habitat.

Dramatically altered hydrologic systems.

Sediment deposition in the wetlands.

Land use and economic activities that are incompatible with the long term maintenance of ecological function.

PROBLEMS ADDRESSED

DataActual Land use cover data from USDA-IL NASS (1999-2007)Elevation (10m x10m resolution).Soil maps (SSURGO) (soil type, crop productivity).Digitized fields within the Big Creek Watershed.Market prices for various crops (1996-2007)Labor and Machinery requirements.

Number of farms: 92Average farm size: 220 acres.Cropland: 7,585 acresPasture: 12,564 acres

Arbitrarily defined farm boundaries using Arc Info (Sengupta et al., 2000).

Soil Loss:USLE Soil loss equation (Wischmeier and Smith 1973)

Typologies of Farmers

• Step 1: Typology of Farmers

Type 1 - Profit MaximizersType 2 – SatisficerType 3 - Conservationist

-- (Kraft et al., 1989)

• Step 2: Distribution of Farm Behavior

Methodology

Satisficer: Bounded rationality (Simon 1957)

X X Con

PM O X

PM O X

Erosion Index

Productivity Index

H M L

L

M

H

X: random assignment for satisficers and conservationist

O: random assignment for profit Max and Satisficers

Farmer typology distribution based on productivity index (CPI) and erosion index

PM : profit maximizerCon: conservationist

Agent Based Model

Endogenous•Labor & machinery

Exogenous variables(Scenario parameters)•Crop prices Policies•Biophysical parameters

Land useOutput

ABM Framework

Create sets of Initial Alternatives(Initial Population)

Evaluate fitness

Choose mates(pairing)

Create offspring (crossover)

Mutate

Repeat

Optimal Solution

Flow Chart- Genetic Algorithm(GA)Human Decision Making Model

Holland (1975)

Genetic Algorithm is

… Computer algorithm

That resides on principles of genetics and evolution

Type1 - Profit MaximizersMaximizing Gross Margin subject to Soil Loss Constraint 2T.

Type 2 – SatisficerMinimizing Soil lossConstraint . Gross Margin greater than goal (satisfaction level).

Satisfaction Level– (one third and three fourth of the profit maximizing level). Randomly assign different satisfaction level to various size farms within the watershed.

Goal: gross margin/acre (parameter that changed based on relative change in commodity prices)

Type 3 – ConservationistMinimizing Soil Loss subject to a Gross Margin Constraint.Gross Margin greater than 0.

Gro

ss M

argi

n

Soil Loss

Graphical Representation

0

4T 3T 2T 0

Goal

A

B

C

A: Profit maximizerB: SatisficerC: Conservationist

ConstraintsLabor

Large Farms:- 1.25 unit of LaborMedium Farms and Small Farms:- 1unit Labor

MachineryLarge Farms: Equipment size was bigger.

Crop Prices

Years (1996-2007)

Land Use ChoicesCorn, Soybean, Alfalfa, Grasslands, CRP tillage type: no-till and conservation tillHistorical landuse Reference: USDA IL- NASS

Historical landuse (2001)

Landscape Farm 1 Farm 2

Objective functionRKLSCP

Gross Margin

Objective functionAgent I: Profit Maximizer Agent II: Satisficer Agent III: Conservationist

Obj: Min soil loss Obj: Minimization

MAX: Gross MarginSubject to: Labor & Machinery

Soil loss <= 2T

MIN: Soil lossSubject to: D>0; &Labor & Machinerywhere D= Gross margin - Goal

MIN: Soil lossSubject to: Labor & Machinery

Gross margin >= 0

Obj: Maximization

. . .

field1 field2 field3 field1 field2 field3 field4Corn Soy Wheat

Create Initial landuse Population

CRP Corn Corn Soy

Farm 2 population

individual 1individual 2individual n

Farm 1 population

Selection Operator

Crossover and Mutation

Field 1 Field 2 Field 3 Field 4Field 1 Field 2 Field 3

If years=3

yes

Stop

NO

Introducing Crop Rotation SequenceVarious options: Last Year LU Present Lu

optionsRule/Cost

1. CRP CRP No-change

2. Soybean corn, pasture, wheat

Reduced fertilizer cost

soybean Possible Reduction in soybean yield

3. Corn corn, soybean, wheat

pasture Increase cost4. Pasture corn, soybean,

wheatIncrease cost

pasture Increase yield and decrease

cost.

Agent Model

Population 1000Generation: 500Cross over probability: 0.6Mutation probability : 0.2

---- time: approximately 5 min

5. Results

Results

Validation of Model

Results : Three year rotation landuse: Historical landuse 2001

2002 2003 2004

Prediction: 80% Prediction: 82% Prediction: 73%

Agent1Profit Maximizer

Agent2Satisficer

Agent 3Conservationist

2002 2003 2004 2002 2003 2004 2002 2003 2004

Correct Prediction

82% 81% 75% 79% 81% 71% 82% 85% 70%

PastureUnder_prediction

11% 12% 11% 2% 2% 3% 6% 7% 4%

Crop Under_prediction

7% 7% 14% 19% 18% 26% 12% 8% 26%

Prediction Based on Agent type

2004 2005 2006

Prediction: 75% Prediction: 84% Prediction: 87%

2004: Corn $2.76/bu; Soy $8.40/bu; Hay $87/ton; CRP 68

2005: Corn $2.29/bu; Soy $6.27/bu; Hay $90.17/ton; CRP 68

2006: Corn $2.61/bu; Soy $6.00/bu; Hay $95.75/ton; CRP 68

Prices

Results : Three year rotation landuse: Historical landuse 2003

Agent1Profit Maximizer

Agent2Satisficer

Agent 3Conservationist

2004 2004 2006 2004 2004 2006 2004 2004 2006

Correct Prediction

84% 86% 84% 68% 80% 86% 71% 83% 91%

PastureUnder_prediction

4% 6% 14% 3% 2% 4% 2% 3% 6%

Crop Under_prediction

13% 8% 2% 28% 18% 10% 27% 13% 1%

Prediction Based on Agent type

Justification for using three agent types:

--Multi Agent model developed here is capturing the reality better than previously developed model of profit maximizing model (GEOLP) developed by Sengupta et al., (2000).

Scenarios 1 3 4 5 6 7 8 9

olicy Scenario=>

Baseline- Ethanol No

Compliance w/

Drought

Ethanol No

Compliance w/o

Drought

Ethanol Complian

ce + riparian

protection, No

drought

Ethanol Complian

ce + riparian

protection + fert tax,

No drought

Baseline w/ ESS

Payments

Baseline w/ ESS

Payments & no 2002 Farm Bill Payments: DP, CC

Ethanol w/ ESS Payments

No Drought

olicy Tool-value / compliance (Plan to keep land at T

if land leaves CRP) 2T 2T 2T T T 2T 1.5T 1.5TPrice of corn $2.30 $5.60 $5.60 $5.60 $5.60 $2.30 $2.30 $5.60

Price of Soybeans $5.60 $13.60 $13.60 $13.60 $13.60 $5.60 $5.60 $13.60 Price of Hay $60.00 $100 $60 $60 $60 $60.00 $60.00 $60

rice & Yield of Switch Grass: $/ton@x eld/acre N N N N N N N N

CRP Rental Rate--Reg $/ac $68.00 $68 $68 $68 $68 $68.00 $68.00 $68 CRP Rental Rate--Contin $/ac $118 $118 $118 N N N N N

ax on Fertilizer % of Fert Costs N N N N 200% N N Nevel of Fert Application Rate lb/AC: N, P, K

N N N N N N N Npayment for riparian area $/ac N N N $150 $150 $150 $150 $150 Carbon Payment for Seq $/T N N N N N $32.19 $32.19 $32.19

arbon Payment for Storage $/T/year: No. of rs amt of payment N N N N N N N Nax per ton of soil loss: $/ton of Soil N N N N $10 N N Nayment for Conservation Practices--CSP doption Fee N N N N N $45 $45 $45 ayment for Wildlife habitat $/ac N N N N N $30 $30 $30 and retention in CRP--Full Period Y/N Y Y Y Y Y Y Y Yermit Hay harvest on CRP: Y, N N N N N N N N Nermit Switch Grass on CRP: Y, N N N N N N N N Novernment Paymentsrect payments Y/N Y Y Y Y Y Y N Yountercyclical Payments Y/N Y Y Y Y Y Y N Y

Comparison of Scenario: Baseline versus Ethanol

Land use (Acres)No-till CornConservation till CornNo-till SoybeansConservation till SoybeansAlfalfa HayCRP

5773,714

1531,375

10,0443,947

3,0005,021

276605

7,2653,516

Comparison of Scenario: Baseline versus Ethanol

Economic ProfitAverage gross margin ($)Average gross margin/acre

24,233117

65,553314

Ecosystem ServicesAverage soil loss (tons)Average carbon sequestration (tons)

78260

89239

Agent TypeProfit maximizerAverage Gross Margin ($)Average Soil Loss (tons)Average carbon sequestration (tons)SatisficerAverage Gross Margin ($)Average Soil Loss (tons)Average carbon sequestration (tons)ConservationistAverage Gross Margin ($)Average Soil Loss (tons)Average carbon sequestration (tons)

33,2021,592

37

19,479175

85

15,152142

72

129,2531,836

(11)

20,927187

83

15,718145

70

6. Conclusions The agent model developed here will help policy and decision-makers

identify the various agents within the watershed and assess various policy options by predicting future land use decisions and production of commodities and ecosystem services resulting from varying market conditions and policies in a multifunctional landscape.

The utilization of genetic algorithms in modeling human behaviors provides clear advantages of flexibility over traditional optimization methods and outperformed previous linear programming analysis using a single profit-maximizing agent

Acknowledgements : Research funded by NSF

Contact: Seth Soman

email: soman.sethuram@dsu.nodak.edu

Questions